Mateusz, there are surprisingly few papers on the subject.  Check out www.CMG.org.  for 2+ year old conference proceedings you don't have to be a member.  ACM Sigmetrics also has publications on QoS.

Maybe I'm doing something wrong but I have to be a member to see conference proceedings. Also I can't find anything about queuing systems with FARIMA...

For proceedings that are 2+ years old, you just need to register, so they know who you are.  They won't spam you; its just for their internal purposes. It is a practitioners' conference; so finding the right papers won't be easy.  Look up by author names: Daniel Menasce; Boris Zibitsker; Neil Gunther; Jeffrey Busen; Uriel Carradquilla; Adrian Cockroft.  These are the classics.  I have coauthored a couple of papers on queueing theory application there as well in 2012, but they may not be available to nonmembers until the cmg'14 conference (the 2-year rule).  By keyword, look for "Erlang"; "overhead"; "capacity sizing"; " Quality of Service" or "QoS"; even "Little's Law" and "Utilization Law".

I spent hours of searching and I think it's to much work only for 4 simple formulas :) If you find any papers on the subject please inform me. And of course thank you for the answers.

It is not too hard to look up "Traffic prediction using FARIMA models":

"Previous traffic measurements have found the coexistence of both long-range and short-range dependence in network traffic. Therefore, models are required to predict traffic that has both long-range and short-range dependence. This paper provides a procedure to model and predict traffic using FARIMA (p,d,q) models. Our experiments illustrate that the FARIMA model is a good model and is capable of capturing the property of actual traffic. We provide guidelines to simplify the FARIMA model fitting procedure and thus to reduce the time of traffic modeling and prediction"

There are a lot of papers on FARIMA traffic modeling (e.g. on IEEE) but there's no analysis and analitycal expressions of QoS parameters such as loss probability, mean queue length or cell delay. I tried to find a general solutions for self-similar inputs but there's no information about FARIMA inputs. I think systems like FARIMA/M/1/K or FARIMA/M/c are not described yet. 

Mateusz, I'm trying to better understand your question.  FARIMA is a way to fit a model into a time series.  The */*/* is Kendall notation indicating the arrival, service, and queueing processes. You can successfully model your traffic with quantile regression, with Holt-Winters, (F)ARIMA, but what matters is the underlying physics, not the model used to predict the traffic.  Look up Erlang and Engset models.  They work very well for QoS.

I do not see any analytic papers on fractional ARIMA calculation. I agree with you that this is a gap. That is PhD work-to-be done. In my queueing paper, we conquered the M/M/r/K/K calculation for Engset and Erlang. It may inspire your work.

"Computational tools for the service systems of self-similar streams" that's the topic of my engineer's diploma paper. I've found  the analysis of systems with Pareto input and FBM input. FARIMA is the third self-similar process to analyze in queuing system. Are there any other types of self-similar processes?